A Theoretical Foundation for the Stakeholder Corporation

Transcription

1 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 1 / 25 A Theoretical Foundation for the Stakeholder Corporation Michael Magill Martine Quinzii Jean Charles Rochet U.S.C U.C. Davis U. Zurich and Toulouse School of Economics Cowles GE Conference

2 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 2 / 25 Corporate objective: Shareholders or Stakeholders Under which of the following assumptions is a large company in your country managed? 1 Shareholder interest should be given the first priority. 2 A firm exists for the interests of all stakeholders. Question to a sample of firms managers (Yoshimuri (1995))

3 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 3 / 25 Models to Support Different Views The anglo-saxon view (UK, US) of the corporation is shared by most professional economists: there is one and only one social responsibility of business to use its resources and engage in activities designed to increase its profits (Friedman 1970).

4 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 3 / 25 Models to Support Different Views The anglo-saxon view (UK, US) of the corporation is shared by most professional economists: there is one and only one social responsibility of business to use its resources and engage in activities designed to increase its profits (Friedman 1970). Shareholder market value maximization does have a theoretical foundation the Arrow-Debreu theory applied to production economies (under uncertainty) and the two theorems of welfare economics.

5 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 3 / 25 Models to Support Different Views The anglo-saxon view (UK, US) of the corporation is shared by most professional economists: there is one and only one social responsibility of business to use its resources and engage in activities designed to increase its profits (Friedman 1970). Shareholder market value maximization does have a theoretical foundation the Arrow-Debreu theory applied to production economies (under uncertainty) and the two theorems of welfare economics. This perhaps explains its predominance as the paradigm in economics and corporate finance.

6 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 4 / 25 Models to Support Different Views We propose an alternative probability model of a stochastic economy with production which provides a foundation for stakeholder view of the corporation.

7 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 4 / 25 Models to Support Different Views We propose an alternative probability model of a stochastic economy with production which provides a foundation for stakeholder view of the corporation. Seminar focuses the simplest model which supports stakeholder view.

8 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 4 / 25 Models to Support Different Views We propose an alternative probability model of a stochastic economy with production which provides a foundation for stakeholder view of the corporation. Seminar focuses the simplest model which supports stakeholder view. Hopefully the next presentation will give opportunity to discuss the difference between this model and the standard state of nature model and when each model is most appropriate.

9 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1

10 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods).

11 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods). At date 0 firm invests a (units of money). Investment is risky.

12 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods). At date 0 firm invests a (units of money). Investment is risky. Uncertainty is modeled through probability of success.

13 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods). At date 0 firm invests a (units of money). Investment is risky. Uncertainty is modeled through probability of success. At date 1, with probability π(a) firm produces with technology f g (l), with probability (1 π(a)) produces with technology f b (l).

14 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods). At date 0 firm invests a (units of money). Investment is risky. Uncertainty is modeled through probability of success. At date 1, with probability π(a) firm produces with technology f g (l), with probability (1 π(a)) produces with technology f b (l). g is the good state: f g(l) > f b (l) = f g(l) > f b (l).

15 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods). At date 0 firm invests a (units of money). Investment is risky. Uncertainty is modeled through probability of success. At date 1, with probability π(a) firm produces with technology f g (l), with probability (1 π(a)) produces with technology f b (l). g is the good state: f g(l) > f b (l) = f g(l) > f b (l). For the seminar, most of the time no labor: f g (l) = y g, f b (l) = y b, l 0. y g π g = π(a) π b = 1 π(a) y b f g (l) f b (l)

16 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 5 / 25 Probability Model of Production One firm, two periods t = 0, 1 Three goods: labor, produced good, money (composite of all other goods). At date 0 firm invests a (units of money). Investment is risky. Uncertainty is modeled through probability of success. At date 1, with probability π(a) firm produces with technology f g (l), with probability (1 π(a)) produces with technology f b (l). g is the good state: f g(l) > f b (l) = f g(l) > f b (l). For the seminar, most of the time no labor: f g (l) = y g, f b (l) = y b, l 0. y g π g = π(a) π b = 1 π(a) y b f g (l) f b (l) y b < y g, π(a) increasing concave in a.

17 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 6 / 25 Agents Two classes of agents continuum (mass 1) of risk neutral investors: endowment: (e i 0, e i 1) and equal share of ownership of the firm. Preferences U i (m) = m i 0 + δ X π sm i s s

18 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 6 / 25 Agents Two classes of agents continuum (mass 1) of risk neutral investors: endowment: (e i 0, e i 1) and equal share of ownership of the firm. Preferences U i (m) = m i 0 + δ X π sm i s s continuum (mass 1) of consumers: endowment: (e c 0, e c 1) preferences U c (m, c) = m c 0 + δ X s π s(u(c s) + m c s)

19 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 6 / 25 Agents Two classes of agents continuum (mass 1) of risk neutral investors: endowment: (e i 0, e i 1) and equal share of ownership of the firm. Preferences U i (m) = m i 0 + δ X π sm i s s continuum (mass 1) of consumers: endowment: (e c 0, e c 1) preferences U c (m, c) = m c 0 + δ X s π s(u(c s) + m c s) quasi-linear preferences: no income effect + risk neutrality. Endowments are sufficiently large for non-negativity constraint on money to be never binding.

20 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 6 / 25 Agents Two classes of agents continuum (mass 1) of risk neutral investors: endowment: (e i 0, e i 1) and equal share of ownership of the firm. Preferences U i (m) = m i 0 + δ X π sm i s s continuum (mass 1) of consumers: endowment: (e c 0, e c 1) preferences U c (m, c) = m c 0 + δ X s π s(u(c s) + m c s) quasi-linear preferences: no income effect + risk neutrality. Endowments are sufficiently large for non-negativity constraint on money to be never binding. aggregate endowment: e 0 = e i 0 + ec 0, e 1 = e i 1 + ec 1

21 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 7 / 25 Market Value Maximizing Equilibrium Markets: at date 1: spot market for produced good; price p g if normal supply, price p b if accident. Competitive pricing.

22 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 7 / 25 Market Value Maximizing Equilibrium Markets: at date 1: spot market for produced good; price p g if normal supply, price p b if accident. Competitive pricing. At date 0: borrowing/lending (can be non-contingent given risk neutrality), equity market. r interest rate, q e price of equity.

23 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 7 / 25 Market Value Maximizing Equilibrium Markets: at date 1: spot market for produced good; price p g if normal supply, price p b if accident. Competitive pricing. At date 0: borrowing/lending (can be non-contingent given risk neutrality), equity market. r interest rate, q e price of equity. Pricing is risk neutral: r = δ, q e = s where a is chosen by the firm. π s (a) p sy s 1 + r a

24 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 7 / 25 Market Value Maximizing Equilibrium Markets: at date 1: spot market for produced good; price p g if normal supply, price p b if accident. Competitive pricing. At date 0: borrowing/lending (can be non-contingent given risk neutrality), equity market. r interest rate, q e price of equity. Pricing is risk neutral: r = δ, q e = s where a is chosen by the firm. π s (a) p sy s 1 + r a Budget constraint of investors m i π s (a)m i s = e i r 1 + r ei 1 + q e s

25 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 7 / 25 Market Value Maximizing Equilibrium Markets: at date 1: spot market for produced good; price p g if normal supply, price p b if accident. Competitive pricing. At date 0: borrowing/lending (can be non-contingent given risk neutrality), equity market. r interest rate, q e price of equity. Pricing is risk neutral: r = δ, q e = s where a is chosen by the firm. π s (a) p sy s 1 + r a Budget constraint of investors m i π s (a)m i s = e i r 1 + r ei 1 + q e s Investors want the firm to maximize q e (p.v. of profit) and are indifferent among all m satisfying the budget constraint.

26 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 8 / 25 Market Value Maximizing Equilibrium (ctd) Consumers: Budget constraint m c r s π s (a)(m c s + p s c s ) = e c r ec 1

27 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 8 / 25 Market Value Maximizing Equilibrium (ctd) Consumers: Budget constraint m c r s π s (a)(m c s + p s c s ) = e c r ec 1 Consumers maximize utility under b.c. FOC: u (c s ) = p s

28 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 8 / 25 Market Value Maximizing Equilibrium (ctd) Consumers: Budget constraint m c r s π s (a)(m c s + p s c s ) = e c r ec 1 Consumers maximize utility under b.c. FOC: u (c s ) = p s Firm maximizes market value a E = argmax s π s (a) p sy s 1 + r a = s π s(a) p sy s 1 + r 1 = 0

29 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 8 / 25 Market Value Maximizing Equilibrium (ctd) Consumers: Budget constraint m c r s π s (a)(m c s + p s c s ) = e c r ec 1 Consumers maximize utility under b.c. FOC: u (c s ) = p s Firm maximizes market value a E = argmax s π s (a) p sy s 1 + r a = s π s(a) p sy s 1 + r 1 = 0 Markets clear: c s = y s, s = g, b (Walras Law +indifference on timing of money consumption = money market clear)

30 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 8 / 25 Market Value Maximizing Equilibrium (ctd) Consumers: Budget constraint m c r s π s (a)(m c s + p s c s ) = e c r ec 1 Consumers maximize utility under b.c. FOC: u (c s ) = p s Firm maximizes market value a E = argmax s π s (a) p sy s 1 + r a = s π s(a) p sy s 1 + r 1 = 0 Markets clear: c s = y s, s = g, b (Walras Law +indifference on timing of money consumption = money market clear) Summary: a E determined by the equation ) π (a E ) (u (y g )y g u (y b )y b = 1 + r

31 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 9 / 25 Optimal Investment a maximizes Social Welfare W(a) = e 0 a + δ( s π s(a)u(y s )) + δe 1

32 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 9 / 25 Optimal Investment a maximizes Social Welfare W(a) = e 0 a + δ( s π s(a)u(y s )) + δe 1 a defined by FOC ( ) π (a ) u(y g ) u(y b ) = 1 + r

33 Magill & Quinzii& Rochet () Stakeholder Corporation April 29 9 / 25 Optimal Investment a maximizes Social Welfare W(a) = e 0 a + δ( s π s(a)u(y s )) + δe 1 a defined by FOC ( ) π (a ) u(y g ) u(y b ) = 1 + r Concavity = u(x) u (x)x increasing (derivative u (x)) = u(y g ) u(y b ) > u (y g )y g u (y b )y b

34 Optimal Investment a maximizes Social Welfare W(a) = e 0 a + δ( s π s(a)u(y s )) + δe 1 a defined by FOC ( ) π (a ) u(y g ) u(y b ) = 1 + r Concavity = u(x) u (x)x increasing (derivative u (x)) = u(y g ) u(y b ) > u (y g )y g u (y b )y b Theorem There is under-investment at MV equilibrium: a E < a Magill & Quinzii& Rochet () Stakeholder Corporation April 29 9 / 25

35 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Inefficiency in NPV maximization Market value maximization by capitalist firm gives FOC ) π (a E ) (u (y g )y g u (y b )y b = 1 + r Social welfare maximization requires FOC ( ) π (a ) u(y g ) u(y b ) = 1 + r

36 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Inefficiency in NPV maximization Market value maximization by capitalist firm gives FOC ) π (a E ) (u (y g )y g u (y b )y b = 1 + r Social welfare maximization requires FOC ( ) π (a ) u(y g ) u(y b ) = 1 + r which can be written as ( ) π (a ) [u(y g ) u (y g )y g ] [u(y b ) u (y b )y b ] }{{} +(u (y g )y g u (y b )y b ) = 1+ }{{}

37 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Inefficiency in NPV maximization Market value maximization by capitalist firm gives FOC ) π (a E ) (u (y g )y g u (y b )y b = 1 + r Social welfare maximization requires FOC ( ) π (a ) u(y g ) u(y b ) = 1 + r which can be written as ( ) π (a ) [u(y g ) u (y g )y g ] [u(y b ) u (y b )y b ] }{{} +(u (y g )y g u (y b )y b ) = 1+ }{{} The social objective takes into account consumer surplus u(c s ) u (c s )c s profit of shareholders p s y s Market-value maximization omits consumer surplus.

38 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Solving Externality Problem Inefficiency of profit max comes from external effect of firm s action a on consumers U c (c, m) = m 0 + s π s(a)(m s + u(c s ))

39 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Solving Externality Problem Inefficiency of profit max comes from external effect of firm s action a on consumers U c (c, m) = m 0 + s π s(a)(m s + u(c s )) Standard solutions for externality 1 government intervention (quantity regulation or tax/subsidy)

40 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Solving Externality Problem Inefficiency of profit max comes from external effect of firm s action a on consumers U c (c, m) = m 0 + s π s(a)(m s + u(c s )) Standard solutions for externality 1 government intervention (quantity regulation or tax/subsidy) 2 internalization through larger entity: integrate parties involved in externality

41 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Solving Externality Problem Inefficiency of profit max comes from external effect of firm s action a on consumers U c (c, m) = m 0 + s π s(a)(m s + u(c s )) Standard solutions for externality 1 government intervention (quantity regulation or tax/subsidy) 2 internalization through larger entity: integrate parties involved in externality 3 create tradeable property rights (Coase)

42 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Stakeholder Equilibrium Since externality only concerns agents associated with the firm, it seems natural to try second approach: enlarge the boundary of the firm to include consumers (and workers).

43 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Stakeholder Equilibrium Since externality only concerns agents associated with the firm, it seems natural to try second approach: enlarge the boundary of the firm to include consumers (and workers). Definition: (c, a, p ) is a (reduced form) stakeholder equilibrium if c = arg max c 0 {u(c) p s c}, s = g, b a = arg max a 0 { 1 1+r s π s(a)(cs(p s) + R(p s)) a} c s = y s

44 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Stakeholder Equilibrium Since externality only concerns agents associated with the firm, it seems natural to try second approach: enlarge the boundary of the firm to include consumers (and workers). Definition: (c, a, p ) is a (reduced form) stakeholder equilibrium if c = arg max c 0 {u(c) p s c}, s = g, b a = arg max a 0 { 1 1+r s π s(a)(cs(p s) + R(p s)) a} c s = y s Changes the objective of firm from max of NPV of profit to max of net p.v. of stakeholder surplus.

45 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Stakeholder Equilibrium Since externality only concerns agents associated with the firm, it seems natural to try second approach: enlarge the boundary of the firm to include consumers (and workers). Definition: (c, a, p ) is a (reduced form) stakeholder equilibrium if c = arg max c 0 {u(c) p s c}, s = g, b a = arg max a 0 { 1 1+r s π s(a)(cs(p s) + R(p s)) a} c s = y s Changes the objective of firm from max of NPV of profit to max of net p.v. of stakeholder surplus. Theorem A stakeholder equilibrium is Pareto optimal

46 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Stakeholder Equilibrium Since externality only concerns agents associated with the firm, it seems natural to try second approach: enlarge the boundary of the firm to include consumers (and workers). Definition: (c, a, p ) is a (reduced form) stakeholder equilibrium if c = arg max c 0 {u(c) p s c}, s = g, b a = arg max a 0 { 1 1+r s π s(a)(cs(p s) + R(p s)) a} c s = y s Changes the objective of firm from max of NPV of profit to max of net p.v. of stakeholder surplus. Theorem A stakeholder equilibrium is Pareto optimal Gives precise content to the stakeholder corporation, already advocated in the final chapter of Berle and Means (1932) The new concept of the corporation.

47 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium

48 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium information: how to find out consumer surplus CS(p s)

49 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium information: how to find out consumer surplus CS(p s) incentives: why would manager maximize stakeholder surplus

50 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium information: how to find out consumer surplus CS(p s) incentives: why would manager maximize stakeholder surplus financing: if NPV of profit is negative, shareholders will not finance investment (limited liability)

51 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium information: how to find out consumer surplus CS(p s) incentives: why would manager maximize stakeholder surplus financing: if NPV of profit is negative, shareholders will not finance investment (limited liability) Our proposal: introduce a market for consumer rights (c-rights) on which agents trade right to buy from the firm

52 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium information: how to find out consumer surplus CS(p s) incentives: why would manager maximize stakeholder surplus financing: if NPV of profit is negative, shareholders will not finance investment (limited liability) Our proposal: introduce a market for consumer rights (c-rights) on which agents trade right to buy from the firm Holders of c-rights are given voting rights in the decisions of the firm.

53 Implementing Stakeholder Equilibrium Three problems for implementing stakeholder equilibrium information: how to find out consumer surplus CS(p s) incentives: why would manager maximize stakeholder surplus financing: if NPV of profit is negative, shareholders will not finance investment (limited liability) Our proposal: introduce a market for consumer rights (c-rights) on which agents trade right to buy from the firm Holders of c-rights are given voting rights in the decisions of the firm. Definition In a Coasian equilibrium management is instructed to maximize the total value equity + consumer rights (+ worker rights) Magill & Quinzii& Rochet () Stakeholder Corporation April / 25

54 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity

55 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity c-rights give right to buy from firm consumers: initial holding of c-rights

56 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity Equity and c-rights traded on markets. c-rights give right to buy from firm consumers: initial holding of c-rights

57 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares c-rights give right to profit give right to buy from firm investors: initial holding of equity consumers: initial holding of c-rights Equity and c-rights traded on markets. What is the value of a c-right on the market?

58 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity Equity and c-rights traded on markets. c-rights What is the value of a c-right on the market? give right to buy from firm consumers: initial holding of c-rights Suppose a quantity η 1 of rights exist. If η < 1 not all consumers have rights and demand changes: spot prices (p g (η), p b (η)).

59 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity Equity and c-rights traded on markets. c-rights What is the value of a c-right on the market? give right to buy from firm consumers: initial holding of c-rights Suppose a quantity η 1 of rights exist. If η < 1 not all consumers have rights and demand changes: spot prices (p g (η), p b (η)). Equilibrium value of c-rights q c (a, η) = δ( s π(a)cs(p s(η))

60 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity Equity and c-rights traded on markets. c-rights What is the value of a c-right on the market? give right to buy from firm consumers: initial holding of c-rights Suppose a quantity η 1 of rights exist. If η < 1 not all consumers have rights and demand changes: spot prices (p g (η), p b (η)). Equilibrium value of c-rights q c (a, η) = δ( s π(a)cs(p s(η)) If there is scarcity of consumer rights, then the value of a consumer right is the consumer surplus.

61 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 c-rights equity shares give right to profit investors: initial holding of equity Equity and c-rights traded on markets. c-rights What is the value of a c-right on the market? give right to buy from firm consumers: initial holding of c-rights Suppose a quantity η 1 of rights exist. If η < 1 not all consumers have rights and demand changes: spot prices (p g (η), p b (η)). Equilibrium value of c-rights q c (a, η) = δ( s π(a)cs(p s(η)) If there is scarcity of consumer rights, then the value of a consumer right is the consumer surplus. if η 1, q c (a) δ s π s(a)cs(p s) (since (p g(η), p b(η)) (p g, p b))

62 c-rights equity shares give right to profit investors: initial holding of equity c-rights give right to buy from firm consumers: initial holding of c-rights Equity and c-rights traded on markets. What is the value of a c-right on the market? Suppose a quantity η 1 of rights exist. If η < 1 not all consumers have rights and demand changes: spot prices (p g (η), p b (η)). Equilibrium value of c-rights q c (a, η) = δ( s π(a)cs(p s(η)) If there is scarcity of consumer rights, then the value of a consumer right is the consumer surplus. if η 1, q c (a) δ s π s(a)cs(p s) (since (p g(η), p b(η)) (p g, p b)) Theorem When η 1 the limit Coasian equilibrium is Pareto optimal. Magill & Quinzii& Rochet () Stakeholder Corporation April / 25

63 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Heterogeneous consumers This result does not hold with heterogeneous consumers.

64 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Heterogeneous consumers This result does not hold with heterogeneous consumers. Utility of consumer of type α, α [0, 1] U(m, c; α) = m 0 + δ π s (a)(u(c, α) + m s ), u α > 0, u cα > 0, Distribution function G over types.

65 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Heterogeneous consumers This result does not hold with heterogeneous consumers. Utility of consumer of type α, α [0, 1] U(m, c; α) = m 0 + δ π s (a)(u(c, α) + m s ), u α > 0, u cα > 0, Distribution function G over types. If (a measure of) η rights are issued then the price reflects the surplus of the marginal buyer ˆα(η) defined by η = 1 ˆα(η) dg(α)

66 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Heterogeneous consumers This result does not hold with heterogeneous consumers. Utility of consumer of type α, α [0, 1] U(m, c; α) = m 0 + δ π s (a)(u(c, α) + m s ), u α > 0, u cα > 0, Distribution function G over types. If (a measure of) η rights are issued then the price reflects the surplus of the marginal buyer ˆα(η) defined by η = 1 ˆα(η) dg(α) If η 1 then price goes to valuation of the lowest type

67 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Heterogeneous consumers This result does not hold with heterogeneous consumers. Utility of consumer of type α, α [0, 1] U(m, c; α) = m 0 + δ π s (a)(u(c, α) + m s ), u α > 0, u cα > 0, Distribution function G over types. If (a measure of) η rights are issued then the price reflects the surplus of the marginal buyer ˆα(η) defined by η = 1 ˆα(η) dg(α) If η 1 then price goes to valuation of the lowest type Either some agents are excluded and this creates an inefficiency, or the price is low (valuation of the lowest type). In all cases the value of consumer rights does not reflect the full value of consumer surplus to all types.

68 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Coasian Equilibrium Objective to be maximized (w.r.t. a, taking η as given) η q c (p(η), a) + q e (p(η), a) or s π s (a) 1 + r (η cs(p s(η), ˆα(η)) + p s (η)y s ) a

69 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Coasian Equilibrium Objective to be maximized (w.r.t. a, taking η as given) η q c (p(η), a) + q e (p(η), a) or s π s (a) 1 + r (η cs(p s(η), ˆα(η)) + p s (η)y s ) a Welfare at Coasian equilibrium W(η) Welfare at capitalist equilibrium W (profit max)

70 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Coasian Equilibrium Objective to be maximized (w.r.t. a, taking η as given) η q c (p(η), a) + q e (p(η), a) or s π s (a) 1 + r (η cs(p s(η), ˆα(η)) + p s (η)y s ) a Welfare at Coasian equilibrium W(η) Welfare at capitalist equilibrium W (profit max) Theorem: Coasian Equilibrium improves on Capitalism Either (i) lim η 1 W(η) > W

71 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Coasian Equilibrium Objective to be maximized (w.r.t. a, taking η as given) η q c (p(η), a) + q e (p(η), a) or s π s (a) 1 + r (η cs(p s(η), ˆα(η)) + p s (η)y s ) a Welfare at Coasian equilibrium W(η) Welfare at capitalist equilibrium W (profit max) Theorem: Coasian Equilibrium improves on Capitalism Either (i) lim η 1 W(η) > W or (ii) lim η 1 W(η) = W and W η (1) < 0, so that for η sufficiently close to 1, W(η) > W.

72 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Why Result Different from Standard AD Efficiency Result? Every probability model has a state space representation (Kolmogorov Theorem) Does it suffice to write the model with the same characteristics on a state space and maximize profit expressed on this space to get Pareto optimality?

73 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Reformulating Model with States of Nature Uncertainty represented by states of nature ω Ω with exogenous probability P ω represents the circumstances which cause the good outcome y g. Production function: { yg if ω Ω y(ω, a) = g (a) y b if ω Ω b (a)

74 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Reformulating Model with States of Nature Uncertainty represented by states of nature ω Ω with exogenous probability P ω represents the circumstances which cause the good outcome y g. Production function: { yg if ω Ω y(ω, a) = g (a) y b if ω Ω b (a) More standard form: { yg if a > ã(ω) y(ω, a) = if a ã(ω) y b

75 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Reformulating Model with States of Nature Uncertainty represented by states of nature ω Ω with exogenous probability P ω represents the circumstances which cause the good outcome y g. Production function: { yg if ω Ω y(ω, a) = g (a) y b if ω Ω b (a) More standard form: { yg if a > ã(ω) y(ω, a) = if a ã(ω) y b Preferences: Z U i (m i ) = m i 0 +δ ω Ω Z m i ωdp(ω); U c (m c, c) = m c 0 +δ (m c ω +u(c ω))dp(ω) ω Ω

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77 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1

78 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1 Price of money in state ω: δp(ω)

79 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1 Price of money in state ω: δp(ω) δ = 1 1+r

80 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1 Price of money in state ω: δp(ω) δ = 1 1+r Price of good available in state ω: δp(ω)p ω, (defines p ω )

81 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1 Price of money in state ω: δp(ω) δ = 1 1+r Price of good available in state ω: δp(ω)p ω, (defines p ω ) Agents maximize utility, firm maximizes profit taking prices as given, and markets clear

82 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1 Price of money in state ω: δp(ω) δ = 1 1+r Price of good available in state ω: δp(ω)p ω, (defines p ω ) Agents maximize utility, firm maximizes profit taking prices as given, and markets clear Profit of the firm ω Ω p ω y(ω, a) dp(ω) a 1 + r

83 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Arrow-Debreu Equilibrium Markets: Standard AD: all markets at date 0: agents buy and sell money for consumption at date 0 and at date 1 in all states ω, consumers buy good for date 1 in state ω, firm sell good in advance, buy investment a. Price of money at date 0 normalized to 1 Price of money in state ω: δp(ω) δ = 1 1+r Price of good available in state ω: δp(ω)p ω, (defines p ω ) Agents maximize utility, firm maximizes profit taking prices as given, and markets clear Profit of the firm ω Ω p ω y(ω, a) dp(ω) a 1 + r First Welfare Theorem: if AD equilibrium exists it is Pareto optimal.

84 Non-Existence of AD equilibrium Theorem An Arrow-Debreu equilibrium does not exist. Magill & Quinzii& Rochet () Stakeholder Corporation April / 25

85 Non-Existence of AD equilibrium Theorem An Arrow-Debreu equilibrium does not exist. Suppose (a, (p ω ) ω Ω ) equilibrium δp(ω)u (c ω ) = δp(ω)p ω and c ω = y(ω, a ) imply p ω = p g if ω Ω g (a ), p ω = p b if ω Ω b (a ) Magill & Quinzii& Rochet () Stakeholder Corporation April / 25

86 Non-Existence of AD equilibrium Theorem An Arrow-Debreu equilibrium does not exist. Suppose (a, (p ω ) ω Ω ) equilibrium δp(ω)u (c ω ) = δp(ω)p ω and c ω = y(ω, a ) imply p ω = p g if ω Ω g (a ), p ω = p b if ω Ω b (a ) Firm has to check that given prices (p ω ) ω Ω there is no profitable deviation. Magill & Quinzii& Rochet () Stakeholder Corporation April / 25

87 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation a < a

88 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation a < a R(a) R(a ) = = r [(π(a ) π(a))p g (y b y g )] (a a ) r [(π(a) π(a ))p g (y g y b )] (a a )

89 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation a < a R(a) R(a ) = = r [(π(a ) π(a))p g (y b y g )] (a a ) r [(π(a) π(a ))p g (y g y b )] (a a ) Profit maximum at a requires R(a) R(a ) 0 for all a < a (A) lim a a R (a) r π (a )p g (y g y b ) 1 0

90 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation Same reasoning when a > a :

91 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation Same reasoning when a > a : R(a) R(a ) = r [(π(a) π(a ))p b (y g y b )] (a a )

92 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation Same reasoning when a > a : R(a) R(a ) = r [(π(a) π(a ))p b (y g y b )] (a a ) Profit max requires (B) lim a a + R (a) r π (a )p b (y g y b ) 1 0

93 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation Same reasoning when a > a : R(a) R(a ) = r [(π(a) π(a ))p b (y g y b )] (a a ) Profit max requires (B) lim a a + R (a) r π (a )p b (y g y b ) 1 0 A and B require p b (y g y b ) p g (y g y b )

94 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Profitable Deviation Same reasoning when a > a : R(a) R(a ) = r [(π(a) π(a ))p b (y g y b )] (a a ) Profit max requires (B) lim a a + R (a) r π (a )p b (y g y b ) 1 0 A and B require p b (y g y b ) p g (y g y b ) But p g < p b : impossible. Because discontinuity of production function at a for ω the profit has different right and left derivatives with a convex kink.

95 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Conclusion Two preconditions for valid theoretical foundation of stakeholder theory of the firm 1 decisions taken by the firms must have an external effect on stakeholders 2 these externalities must not be readily resolved by government intervention (regulation or taxation).

96 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Conclusion Two preconditions for valid theoretical foundation of stakeholder theory of the firm 1 decisions taken by the firms must have an external effect on stakeholders 2 these externalities must not be readily resolved by government intervention (regulation or taxation). Such conditions are fulfilled if firms are large and influence the probability distribution of their outcomes

97 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Conclusion Two preconditions for valid theoretical foundation of stakeholder theory of the firm 1 decisions taken by the firms must have an external effect on stakeholders 2 these externalities must not be readily resolved by government intervention (regulation or taxation). Such conditions are fulfilled if firms are large and influence the probability distribution of their outcomes Another model with this characteristic: Allen-Carletti-Marquez (2009)

98 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 To obtain an operational stakeholder theory, three additional conditions must be satisfied 1 assign well-defined benefits for each group of stakeholders

99 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 To obtain an operational stakeholder theory, three additional conditions must be satisfied 1 assign well-defined benefits for each group of stakeholders 2 exhibit a way of assigning relative weights to the benefits to obtain a well-defined objective for a firm

100 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 To obtain an operational stakeholder theory, three additional conditions must be satisfied 1 assign well-defined benefits for each group of stakeholders 2 exhibit a way of assigning relative weights to the benefits to obtain a well-defined objective for a firm 3 provide incentives to the firm s manager to maximize this objective.

101 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 To obtain an operational stakeholder theory, three additional conditions must be satisfied 1 assign well-defined benefits for each group of stakeholders 2 exhibit a way of assigning relative weights to the benefits to obtain a well-defined objective for a firm 3 provide incentives to the firm s manager to maximize this objective. Otherwise stakeholder concerns leave firms open to manipulation by management Management can almost always rationalize any action by invoking its impact on the welfare of some stakeholder (Tirole, Econometrica, 2001)

102 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 To obtain an operational stakeholder theory, three additional conditions must be satisfied 1 assign well-defined benefits for each group of stakeholders 2 exhibit a way of assigning relative weights to the benefits to obtain a well-defined objective for a firm 3 provide incentives to the firm s manager to maximize this objective. Otherwise stakeholder concerns leave firms open to manipulation by management Management can almost always rationalize any action by invoking its impact on the welfare of some stakeholder (Tirole, Econometrica, 2001) Stakeholder theory plays into the hands of managers by allowing them to pursue their own interests at the expense of the firm s financial claimants and society at large... (Jensen, Journal of Applied Corporate Finance, 2001)

103 Magill & Quinzii& Rochet () Stakeholder Corporation April / 25 Theoretical answer to (1) profit=interests of shareholders consumer surplus=interests of consumers worker surplus=interest of workers objective: sum of profit, consumer and worker surpluses However surpluses are difficult to evaluate Hence the proposal for creating marketed consumer and worker rights which reveal surpluses